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Transcript
Ecology Letters, (2003) 6: 623–630
REPORT
The role of plant species in biomass production
and response to elevated CO2 and N
Joseph M. Craine1*,
Peter B. Reich2, G. David Tilman1,
David Ellsworth3, Joseph
Fargione1, Johannes Knops4 and
Shahid Naeem5
1
Department of Ecology,
Evolution and Behavior,
University of Minnesota, Saint
Paul, MN 55108, USA
2
Department of Forest
Resources, University of
Abstract
In an experiment that factorially manipulated plant diversity, CO2, and N, we quantified
the effects of the presence of species on assemblage biomass over 10 time points
distributed over 5 years. Thirteen of the 16 species planted had statistically significant
effects on aboveground and/or belowground biomass. Species differed dramatically in
their effects on biomass without any relationship between aboveground and belowground effects. Temporal complementarity among species in their effects seasonally,
successionally, and in response to a dry summer maintained the diversity–biomass
relationships over time and may be the cause behind higher diversity plots having less
variation in biomass over time. The response of plant biomass to elevated N, but not
CO2, was at times entirely dependent on the presence of a single species.
Minnesota, Saint Paul, MN
55108, USA
3
School of Natural Resources
Keywords
BioCON, biodiversity, Cedar Creek Natural History Area, grassland, global change.
and Environment, University of
Michigan, Ann Arbor, MI 48109,
USA
4
School of Biological Sciences,
University of Nebraska, Lincoln,
NE 68588, USA
5
Department of Biology,
University of Washington,
Seattle, WA 98195, USA
*Correspondence: E-mail:
[email protected]
Ecology Letters (2003) 6: 623–630
INTRODUCTION
Ecosystems worldwide are shifting in plant composition
and diversity as they lose native species and non-native
species invade or are introduced (Chapin et al. 2000).
Simultaneously, ecosystems are also being subjected to
increasingly greater supplies of atmospheric CO2 and
inorganic nitrogen (N) (Vitousek 1994; Sala et al. 2000;
Shaw et al. 2002). The productivity of an ecosystem and its
response to elevated atmospheric CO2 and N deposition
depend on the richness and composition of the plant
assemblage (Hector et al. 1999; Niklaus et al. 2001; Tilman
et al. 2001; Reich et al. 2001a; He et al. 2002). Yet, our
ability to understand ecosystem responses to changes in
CO2, N, or plant diversity is limited by our understanding
of the roles of individual species and species interactions
in the functioning of ecosystems with diverse plant
assemblages.
For example, the greater productivity of high diversity
assemblages is caused more by complementarity than by
sampling effects (Loreau & Hector 2001; Tilman et al. 2001),
yet how species interactions generate complementarity is
poorly understood. The lack of understanding of these
interactions is especially acute for aggregate properties of
the ecosystem, such as belowground biomass accumulation,
for which the contribution of individual species cannot be
directly measured. Even if at any one point in time plots
with higher plant diversity have greater biomass because of
the increasing likelihood of a given species being present at
high diversity (i.e. sampling effect) (Aarssen 1997; Huston
1997), different species could be important at different
times. Species can have differential importance along the
developmental sequence of an assemblage (Niklaus et al.
2001), can be offset phenologically (Tilman et al. 2001), and
respond to weather and climate fluctuations differently
(Tilman & Downing 1994). Similarly, the response of an
2003 Blackwell Publishing Ltd/CNRS
624 J. M. Craine et al.
assemblage to elevated CO2 or N can be dependent on the
diversity of the assemblage (Reich et al. 2001a), but any role
of individual species in determining the assemblage
responses to increases in CO2 or N have not been
quantified.
We created a grassland experiment in 1997 in central
Minnesota, USA that factorially combines plant diversity,
atmospheric CO2, and N supply (Reich et al. 2001a). The
experiment is designed in a manner that allows detection of
the effects of individual species (Allison 1999). The study
includes 359 2 · 2 m plots distributed among six 20-m
diameter experimental units (rings). Three rings were
exposed to ambient CO2 concentrations (368 lmol mol)1)
and three to elevated CO2 (560 lmol mol)1) using a free-air
CO2 enrichment (FACE) system. Soils for the experiment
were sandy and each plot was planted in 1997 with one,
four, nine, or 16 local species of C3 grasses, C4 grasses, C3
legumes, C3 non-leguminous dicots (forbs). Half of the plots
received the equivalent of 4 g N m)2 year)1 in the form of
NH4NO3 over three applications each year. In each plot
aboveground biomass and belowground biomass were
harvested biennially (mid-June and early August) from
1998 to 2002. Other results from this study are reported in
(Craine & Reich 2001; Craine et al. 2001; Lee et al. 2001;
Tjoelker et al. 2001; Reich et al. 2001a,b).
Here, we examine the roles of individual species in
determining assemblage-level biomass across a gradient of
planted diversity at different resource availabilities over 10
harvests spread across 5 years. We use statistical techniques
that quantify the effects of the presence of species and
treatments on aboveground and belowground plant biomass
without separating the production of a given species and its
effects on the production of other species.
If species differ in their effects over time, we examine
whether these temporal effects are due largely to ÔÔseasonalÕÕ
differences, ÔÔsuccessionalÕÕ differences, or associated with
interannual variation in climate. We refer to consistent
differences in species effects between the June and August
harvests as ÔÔseasonalÕÕ differences. Successional differences
(sensu Niklaus et al. 2001) in species effects are defined as
differences over time that cannot be attributed to variation
in short-term climate fluctuations and more likely reflect
differences in growth rate and life history characteristics
among species or ecosystem properties (e.g. N cycling rates).
These transient changes in species effects are not associated
with the immigration of new species, which can be an
important aspect of succession outside of experiments that
control species pools.
An important consequence in variation in species effects
and interactions among species over time is its effect on the
variability over time in assemblage biomass. For example,
species effects can be temporally complementary and
variation in biomass over time will decrease with increasing
2003 Blackwell Publishing Ltd/CNRS
diversity due to the greater likelihood of more diverse plots
containing species with temporally complementary effects.
To explore questions of the role of individual species in the
responses of assemblages to elevated CO2 and N, we test
for statistical interactions between the presence of species
and resource treatments that signify differences in biomass
response of assemblages based on the presence or absence
of a species.
MATERIALS AND METHODS
The BioCON experiment is located at the Cedar Creek
Natural History Area in Minnesota, USA. Plots were
established on a secondary successional grassland on sandy
soil. Before seeding, plots were tilled, methyl bromide was
applied to kill weed seeds, and soils were reinoculated with
unfumigated soil. The 16 species used in this study were all
native or naturalized to the Cedar Creek Natural History
Area and include four C4 grasses (Andropogon gerardii,
Bouteloua gracilis, Schizachyrium scoparium, Sorghastrum nutans),
four C3 grasses (Agropyron repens, Bromus inermis, Koeleria
cristata, Poa pratensis), four N-fixing legumes (Amorpha canescens, Lespedeza capitata, Lupinus perennis, Petalostemum villosum)
and four non-N-fixing herbaceous species (forbs) (Achillea
millefolium, Anemone cylindrica, Asclepias tuberosa, Solidago rigida).
A split plot design was used with CO2 treatment as the
whole-plot factor, replicated three times among the six
rings. The subplot factors of species number and N
treatment were randomly assigned and replicated in individual plots among the six rings. CO2 was added in elevated
treatments during all daylight hours generally from early
April to late October. Beginning in 1998, half of the plots
were amended with 4 g N m)2 year)1, applied over three
dates each year. Each plot was planted in 1997 with
12 g m)2 of seed partitioned equally among all species
planted in a plot. Plots were regularly weeded to remove
unwanted species. Monocultures of all species were replicated twice within all four CO2 and N treatment combinations. The four- and nine-species plots included both
random selections from all species and those that were
created to enhance contrasts among functional groups. All
plots were burned in the spring of 2000 and 2002.
Aboveground biomass was assessed from a 0.1 m2 strip
of vegetation clipped from each plot and biomass was
separated into species. Belowground biomass was assessed
from three 5 cm diameter · 20 cm deep cores. No one area
was sampled for aboveground or belowground biomass
twice.
All data analyses were conducted in JMP 4.0 (SAS
Institute, Cary, NC, USA). To determine whether biomass
increased or decreased with diversity, biomass was regressed
against the square root transform of planted diversity. For
most simple regressions testing whether biomass increases
Plant species effects, CO2, and N 625
or decreases with planted diversity, CO2 and N treatments
were not included as factors in the model, unless otherwise
mentioned.
A repeated measures ANOVA was used to determine the
main effects of species and treatments on biomass and
statistical interactions between main effects. All main
effects were included initially in the models. These
included the presence/absence of the CO2 treatment, the
N treatment, and each species in the seed mix. As nested
factors (CO2 treatment and ring identity) cannot be
included in repeated measures, we did not include block
identity in the model. Non-significant factors were
removed from the model serially in order of increasing
F, calculating new F values each time a factor is removed.
Owing to the large number of factors and the potential for
false positive results, a more stringent than usual test of
significance was used (P ‡ 0.01). For the remaining
significant main effects (P < 0.01), another model was
constructed that included all significant main effects and all
potential pairwise interactions among the significant main
effects. Non-significant interactions were removed serially
in order of increasing F until all the retained variables had
P < 0.01. The well-balanced design of the experiment with
a large number of plots with contrasting composition leads
to low levels of collinearity among presences of species
and species pairs [low variance inflation factors; see
Schmid et al. (2002) for a discussion of relevant issues].
This allows main effects and interactions to be tested nonsequentially (Type I SS), although we do test the
importance of species richness against the residuals of
the models, since the presences of the significant main
effects and interactions are highly collinear with richness.
The results of the ANOVA are a statistical description of
the effects of the presence/absence of species and
treatments on plot-level biomass. In the ANOVA, the
intercept of the model approximates the biomass of the
average monoculture with no resource treatments, a
significant main effect the change in biomass when that
factor (such as the presence of a particular species) is
present, and a significant statistical interaction among two
factors (such as the presence of a pair of species) alters the
biomass when both factors are present relative to the sum of
the two main effects.
Using the ANOVA approach, a positive statistical interaction implies that the presence of two species yields more
biomass than was expected based on the sum of their
individual effects. A negative statistical interaction implies
that the presence of the two species yields less biomass than
was expected based on the sum of their individual effects.
Both positive and negative statistical interactions could be
indicative of species interactions that cause overyielding.
Thus determining whether a pair of species has complementary or facilitating interactions requires examination of
both the sign and magnitude of the main effects and
statistical interaction. Instead of showing each main effect
and the statistical interactions a species was involved in, for
visualizing the effects of species over time, we calculated the
main effect of the species at a given harvest and added one
half of each statistical interaction of which the species was a
part. This represents the average effect of a species for when
the other species of the statistical interaction was and was
not present in the seed mix.
To examine the consequences of not having slowgrowing species that increase their effects over time, we
also calculated what the change in biomass with increasing
diversity would have been if slow-growing species and
interactions involving slow-growing species had not
increased their effects over time. We determined the
patterns of effects over time using principal components
analyses (PCA). A matrix of the estimates of the main
effects and statistical interactions both aboveground and
belowground (columns) vs. time (rows) were included in the
PCA and the analysis run on the correlations among factors.
One of the principal components separated slow- and fastgrowing species. We then compared the slopes of the
relationships between diversity and (1) mean biomass and
(2) predicted biomass without the eight effects that increase
the most over time (eight most positive aboveground factors
of PCA Axis 1).
We analysed the variance of biomass over time by
determining the standard deviation (SD) of biomass for each
plot over time, determining the relationship between the
SDs and average plot biomass at each diversity level, and
comparing it at a common biomass for the four diversity
levels (least squares mean). We used a regression model that
tested the effects of diversity (categorical), CO2, N, and the
mean biomass of the plot. This standardizes the SD at a
common biomass in a manner that is equivalent to analysing
the coefficients of variation, without being subject to
inflation of ratios and controlling for differences in biomass
among diversity levels. Differences in variance at different
diversity levels can be due to compositional differences
(McGrady-Steed et al. 1997; Naeem & Li 1998; Wardle
1998), which we do not separate out here. As such, whether
reliability or stability increases or decreases with increasing
diversity we cannot answer since we are not partitioning
variance associated with compositional differences, only
whether the variance of the plots increased or decreased
with increasing diversity.
RESULTS
In a regression of aboveground biomass on planted
diversity, aboveground biomass significantly increased with
greater species richness for nine of the 10 harvests
(P < 0.001 for all harvests except August 2000, P ¼ 0.67;
2003 Blackwell Publishing Ltd/CNRS
626 J. M. Craine et al.
Fig. 1). In 2000, May–July precipitation was half of the
precipitation experienced over the same period in 1999 or
2001 and volumetric soil moisture was often at 4%
(P. Reich, unpublished data). A diversity effect was not
present aboveground in August 2000 at any combination of
CO2 or N. Belowground, biomass increased with diversity
for all 10 harvests (P < 0.001). Although the diversity effect
was variable in absolute and relative strength over time,
there appeared to be no monotonic change in the strength
of the diversity effect over time as it was generally
maintained both aboveground and belowground throughout
the 5 years of sampling (Fig. 1).
Based on the repeated measures ANOVA, the presence of
12 species (three C3 grasses, two C4 grasses, three forbs, and
four legumes) significantly (P < 0.01) affected aboveground
biomass (Fig. 2). There was a wide range in the effects of
the presence of species at a given harvest, from )158 g m)2
(Bouteloua, August 2000) to +446 g m)2 (Lespedeza, August
2002). The effects of a single species varied considerably
over time. For example, among the 10 harvests, the effect of
Lespedeza varied by 456 g m)2 and that of Lupinus by
376 g m)2. Averaged across harvests, the model describes
aboveground biomass at each diversity level within 6% of
the mean and little of the variance of the model’s residuals
(1%) is explained by species richness. This implies that the
main effects and interactions of the model capture the
general relationship between diversity and aboveground
biomass.
Figure 1 Aboveground (a) and belowground (b) biomass for the
June (J) and August (A) harvests of the 5 years (1998–2002) for
one-, four-, nine-, and 16-species plots (left to right).
2003 Blackwell Publishing Ltd/CNRS
For belowground biomass, averaged across harvests, the
model predicted belowground biomass within 5% at each
diversity level and diversity explained only 1% of the
variance of the residuals of the repeated measures model.
Nine species significantly altered belowground biomass
(Fig. 2), ranging from )260 g m)2 (Lupinus June 2001) to
+830 g m)2 (Poa June 2001). These included three C3
grasses, two C4 grasses, two forbs, and two legumes. The
effects of the presence of a given species varied by as much
as 557 g m)2 over the 10 harvests. There was only a weak
negative relationship between effects of species aboveground and belowground (P ¼ 0.04, r2 ¼ 0.06) for those
eight species that affected both significantly.
The effects of most species pairs were additive. Only nine
of the 132 possible pairwise interactions for species effects
aboveground were significant and nine of 72 belowground.
The majority of the significant interactions between species
effects on biomass were negative, especially those between
species that had large positive effects (Fig. 3). Negative
interactions between effects produce diminishing increases
in biomass with increasing diversity. If there were no
statistical interactions between species with positive main
effects, biomass would increase linearly with diversity. If
there were positive statistical among species that had
positive main effects, biomass would increase exponentially
over the diversity range of the experiment.
Over the 5 years, the consistently positive diversity effect
is maintained in part by more diverse plots being more likely
to have species that differ in their relative growth rate and/
or seasonal phenology. For example, if slow-growing species
were not present, the diversity effect would have declined in
strength over time both aboveground and belowground.
The slope of the square-root transformed diversity–biomass
relationship would have declined significantly over time if
slow-growing species had not increased their effects beyond
the June 1998 values [r2 ¼ 0.48, Ftime ¼ 7.6, P ¼ 0.02 with
time coded continuously equivalent to harvest number
(1–10)]. Similarly, belowground, the diversity effect would
have been less in later harvests without slow-growing
species increasing their effects beyond those of the first
harvest (r2 ¼ 0.57, Ftime ¼ 10.8, P ¼ 0.01). For example,
instead of a 460 ± 53 g m)2 belowground increase in
biomass from one to 16 species in August 2002, biomass
would have only increased 180 ± 29 g m)2.
Seasonal offsets in effects between cool- and warmseason species is another factor that maintains diversity
effects over time (Fig. 2). Aboveground, species such as
the cool-season Lupinus have consistently more positive
effects in June than August, while the converse is true for
species such as warm-season Lespedeza. Belowground
species such as the cool-season C3 forb Achillea and the
warm-season C4 grass Andropogon were offset seasonally in
their effects.
Plant species effects, CO2, and N 627
Figure 2 Effects of the presence of species on aboveground (a) and belowground (b) biomass for each of the 10 harvests (June 1998–August
2002, left to right). Species effects were calculated as the estimates of the main effects plus one half of the estimates of any interactions with
other species. Included are the results from the repeated measures analysis that denotes whether there were significant effects of species on
average (Avg) across all harvests (between-subjects effects) and whether the effects varied significantly over time (Time; within-subjects
effects). For all factors, between-subjects and within-subjects effects were significant aboveground (between: F-test, F ¼ 24.9, P < 0.001;
within: WilksÕ Lambda, F ¼ 4.5, P < 0.001) and belowground (between: F-test, F ¼ 55.3, P < 0.001; within: WilksÕ Lambda, F ¼ 3.6,
P < 0.001).
Although some species were able to maintain or increase
their effects during the dry 2000 summer (e.g. Petalostemum),
there was insufficient compensatory growth aboveground
by these species to maintain the diversity effect. Species
such as Agropyron and Poa had much more negative effects
on biomass after the dry 2000 summer than during other
times (Fig. 2).
Variance in biomass over time for plots of different
diversity can be due to differences in assemblage composition or differences in the production of individual species
for plots of different diversity. Although we could not
separate the influence of these two sources of variation, the
biomass of high diversity plots showed less variance both
aboveground (P < 0.001; SD ¼ 168, 142, 118, 109 for one-,
four-, nine-, 16-species plots compared at the mean
biomass) and less variance belowground (P ¼ 0.03,
SD ¼ 272, 286, 251, 243).
Different species were not only important in generating
the positive diversity effect, but also in the biomass response
of ecosystems to elevated CO2 and N. The N response of
belowground biomass was dependent on the presence of the
C3 grass Poa (Fig. 4). In the repeated measures ANOVA,
averaged across the 10 harvests, elevated N increased
belowground biomass by 58 g m)2 when Poa was not
present, although there was nearly no N effect during 1998
and 1999. On average, when Poa was present, N increased
biomass by 286 g m)2. Aboveground, the opposite pattern
occurred during 2000–2002, when the presence of Lespedeza
decreased the N effect (+81 g m)2 vs. )10 g m)2) (Fig. 4).
Although there were interactions between N supply and
individual species, N treatment remained significant in the
repeated measures ANOVA models, implying that there was
still a significant response of biomass to elevated N when
the above-mentioned species were not present. Although
elevated CO2 increases aboveground biomass and belowground biomass on average (+15 g m)2 and +52 g m)2),
the response of biomass was not altered by the presence of
any individual species.
2003 Blackwell Publishing Ltd/CNRS
628 J. M. Craine et al.
Figure 3 Relationship between the effects of two species on above
(j) and belowground (h) biomass if there is no statistical
interaction and main effects are additive (x-axis) and when
statistical interactions are included ( y-axis). Each point represents
the effects of two species that a significant statistical interaction in
the repeated measures ANOVA on biomass for a given harvest. The
1 : 1 line represents the relationship if there was no statistical
interaction between species (additive effects). Points to the left are
positive statistical interactions between species effects, to the right
are negative.
DISCUSSION
In a world experiencing increasing CO2 and N, and shifting
composition and diversity, there is great complexity in the
roles of individual species and their interactions with other
species in diverse assemblages. In many cases, the functioning of the communities at different diversity levels are
much more complex than a simple sampling effect in which
the presence of one species generates an increase in biomass
with increasing diversity. Thirteen of the 16 species that we
planted had statistically significant effects on aboveground
and/or belowground biomass. Although the magnitude of
some of the species effects could be at times small, even rare
species can affect the functioning of ecosystems (Lyons &
Schwartz 2001) and thus it is difficult to infer biological
significance from statistical significance. The species that
had no statistical significance on either aboveground or
belowground biomass (Koeleria, Sorghastrum, Anenome) are
fairly different ecologically and we can offer no potential
generalizations about which species are not likely to affect
assemblage biomass.
Species differed in their effects seasonally, during the
transient dynamics of community development (successionally), and in response to climatic variation. Collectively, these
complementary species effects on assemblage biomass
2003 Blackwell Publishing Ltd/CNRS
Figure 4 Dependence of N effects on aboveground biomass on
the presence of Lespedeza [with Lespedeza (j) and without Lespedeza
(h)] and of N effects on belowground biomass on the presence of
Poa [with Poa (j) and without Poa (h)] over the 10 harvests [June
1998 (J98)–August 2002 (A02)].
caused more species-rich assemblages to maintain higher
levels of biomass over time with less variability than less
diverse assemblages. Diverse plots are more likely to have
species that are offset in their seasonality of production,
successional status, or response to variation in climate, such
that a decrease in the production of one species is
compensated for by an increase in production by another
species.
Niklaus et al. (2001) also found that communities that had
a more diverse mix of fast- and slow-growing species
maintained greater productivity over time. In their study,
fast-growing species had high productivity early in the
experiment when nitrogen availability was high and after a
few years they were replaced by slow-growing species as
nitrogen availability declined. In our experiment, N availability declined over time, too (P. Reich unpublished). The
decline in the effects of fast-growing species was not due
solely to the increase in slow-growing species. Even in
monoculture, the biomass of species such as Agropyron and
Bromus declined after 1998 (data not shown). The lack of
interaction between the fast-growing species and N addition
(except Poa) implies that N fertilization did not reverse these
species declines, but does not necessarily mean that a
decrease in N supply is not responsible for the decline of
fast-growing species since the decrease in N supply over
time may have been greater than the N addition rate.
Plant species effects, CO2, and N 629
Even if the successional patterns that we observed were
associated with changes in N availability, these transient
effects are not limited to experiments. In many grasslands, a
large fraction of the ground is disturbed each year by
animals (e.g. gophers at Cedar Creek) and would experience
situations that are qualitatively similar to establishment in
BioCON – bare soil with high nutrient availability. The
relatively weaker initial biodiversity effect in an experiment
in an adjacent field at Cedar Creek (Tilman et al. 2001) may
be due to a lack of performance from fast-growing species
due to either soil or climatic conditions during the first few
years.
Statistical interactions between main effects indicate a
significant change in biomass when both species are present
relative to what was expected based on their individual
effects, causing main effects to be non-additive. Generally,
there were negative interactions between species that had
positive effects and these interactions were more negative
the larger the sum of the main effects, although having both
species still led to greater biomass than if just one of the
species was present. This specific pattern of negative
statistical interactions leads to an asymptotic relationship
between diversity and biomass whereby there are diminishing increases in biomass as the likelihood of negative
statistical interactions increases with increasing diversity. As
a particular statistical interaction does not necessarily imply
inhibition or facilitation, more detailed analyses of the
intercepts, main effects, and interactions are needed, but are
beyond the scope of this paper. A minority of interactions
were positive in sign, but these generally involved species
that had negative main effects, such as the legumes. This
indicates that the negative effects of the species were not as
severe in the presence of the other species.
The response of assemblages to increased resource
availability has been shown to be greater for high diversity
communities (Reich et al. 2001a). We show that this
response is often dependent on the presence of a single
species, which low diversity assemblages are less likely to
have. In the first harvests, there was virtually no response in
belowground biomass to N unless Poa was present, while in
later harvests there was virtually no response in aboveground biomass to N unless Lespedeza wasn’t present. The
N2-fixing legume Lespedeza is likely to decrease its
N2-fixation when inorganic N is added, such that the
additional N has a direct effect on production, but less of a
net effect due to compensatory decreases in N2-fixation.
Although a statistical interaction between CO2 and diversity
was detected by Reich et al. (2001a), no one species was
found to be responsible for this. This may imply multiple
weak interactions between individual species and elevated
CO2.
In conclusion, these results make a strong case for
maintaining diverse plant assemblages and not just attempt-
ing to determine the ÔÔbestÕÕ species to maintain for a given
location. The effects and interactions among species in
diverse assemblages are complex and there was great
complementarity among species in seasonal, successional,
and climatic response differences with little relationship in
species effects aboveground and belowground. While
responses of assemblage biomass to N were dependent on
the presence of individual species, responses to CO2 could
not be ascribed to an individual species. How the BioCON
species affect other aspects of the ecosystem such as N
cycling (Niklaus et al. 2001; Mulder et al. 2002) and invasion
resistance (Knops et al. 1999; Dukes 2001; Kennedy et al.
2002) remains to be seen, but is likely to further show the
individuality of species.
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Editor, I. F. Woodward
Manuscript received 29 January 2003
First decision made 5 March 2003
Manuscript accepted 31 March 2003